SET007 Axioms: SET007+242.ax


%------------------------------------------------------------------------------
% File     : SET007+242 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Filters - Part I
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : filter_0 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  128 (  14 unit)
%            Number of atoms       : 1007 (  61 equality)
%            Maximal formula depth :   24 (   9 average)
%            Number of connectives : 1065 ( 186 ~  ;   4  |; 497  &)
%                                         (  23 <=>; 355 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   40 (   1 propositional; 0-4 arity)
%            Number of functors    :   32 (   0 constant; 1-4 arity)
%            Number of variables   :  349 (   0 singleton; 337 !;  12 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_filter_0,axiom,(
    ? [A] :
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A)
      & v3_filter_0(A) ) )).

fof(cc1_filter_0,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v3_filter_0(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v11_lattices(A)
          & v12_lattices(A) ) ) ) )).

fof(fc1_filter_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k5_filter_0(A,B,C)) ) )).

fof(fc2_filter_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A) )
     => ( ~ v3_struct_0(k8_filter_0(A,B))
        & v3_lattices(k8_filter_0(A,B))
        & v4_lattices(k8_filter_0(A,B))
        & v5_lattices(k8_filter_0(A,B))
        & v6_lattices(k8_filter_0(A,B))
        & v7_lattices(k8_filter_0(A,B))
        & v8_lattices(k8_filter_0(A,B))
        & v9_lattices(k8_filter_0(A,B))
        & v10_lattices(k8_filter_0(A,B)) ) ) )).

fof(t1_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_lattices(A,B,C)
                   => ( r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,D,C))
                      & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,D))
                      & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,D,C))
                      & r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,C,D)) ) ) ) ) ) ) )).

fof(t2_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_lattices(A,B,C)
                   => ( r3_lattices(A,k4_lattices(A,B,D),C)
                      & r3_lattices(A,k4_lattices(A,D,B),C) ) ) ) ) ) ) )).

fof(t3_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_lattices(A,B,C)
                   => ( r3_lattices(A,B,k3_lattices(A,D,C))
                      & r3_lattices(A,B,k3_lattices(A,C,D)) ) ) ) ) ) ) )).

fof(t4_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r3_lattices(A,B,C)
                          & r3_lattices(A,D,E) )
                       => ( r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,E))
                          & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,E,C)) ) ) ) ) ) ) ) )).

fof(t5_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r3_lattices(A,B,C)
                          & r3_lattices(A,D,E) )
                       => ( r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,C,E))
                          & r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,E,C)) ) ) ) ) ) ) ) )).

fof(t6_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_lattices(A,B,C)
                      & r3_lattices(A,D,C) )
                   => r3_lattices(A,k3_lattices(A,B,D),C) ) ) ) ) ) )).

fof(t7_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_lattices(A,B,C)
                      & r3_lattices(A,B,D) )
                   => r3_lattices(A,B,k4_lattices(A,C,D)) ) ) ) ) ) )).

fof(d1_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( m1_filter_0(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                    <=> r2_hidden(k4_lattices(A,C,D),B) ) ) ) ) ) ) )).

fof(t8_filter_0,axiom,(
    $true )).

fof(t9_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( m1_filter_0(B,A)
          <=> ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( ( r2_hidden(C,B)
                          & r2_hidden(D,B) )
                       => r2_hidden(k4_lattices(A,C,D),B) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( ( r2_hidden(C,B)
                          & r3_lattices(A,C,D) )
                       => r2_hidden(D,B) ) ) ) ) ) ) ) )).

fof(t10_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_filter_0(D,A)
                 => ( r2_hidden(B,D)
                   => ( r2_hidden(k3_lattices(A,B,C),D)
                      & r2_hidden(k3_lattices(A,C,B),D) ) ) ) ) ) ) )).

fof(t11_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & r2_hidden(C,B) ) ) ) )).

fof(t12_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v14_lattices(A)
              & l3_lattices(A) )
           => r2_hidden(k6_lattices(A),B) ) ) ) )).

fof(t13_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v14_lattices(A)
          & l3_lattices(A) )
       => m1_filter_0(k6_domain_1(u1_struct_0(A),k6_lattices(A)),A) ) ) )).

fof(t14_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( m1_filter_0(k6_domain_1(u1_struct_0(A),B),A)
           => v14_lattices(A) ) ) ) )).

fof(t15_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => m1_filter_0(u1_struct_0(A),A) ) )).

fof(d2_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k1_filter_0(A) = u1_struct_0(A) ) )).

fof(t16_filter_0,axiom,(
    $true )).

fof(t17_filter_0,axiom,(
    $true )).

fof(t18_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(B,k2_filter_0(A,C))
              <=> r3_lattices(A,C,B) ) ) ) ) )).

fof(t19_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(B,k2_filter_0(A,B))
                & r2_hidden(k3_lattices(A,B,C),k2_filter_0(A,B))
                & r2_hidden(k3_lattices(A,C,B),k2_filter_0(A,B)) ) ) ) ) )).

fof(t20_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v13_lattices(A)
          & l3_lattices(A) )
       => k1_filter_0(A) = k2_filter_0(A,k5_lattices(A)) ) ) )).

fof(d4_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( v1_filter_0(B,A)
          <=> ( B != u1_struct_0(A)
              & ! [C] :
                  ( m1_filter_0(C,A)
                 => ( r1_tarski(B,C)
                   => ( C = u1_struct_0(A)
                      | B = C ) ) ) ) ) ) ) )).

fof(t21_filter_0,axiom,(
    $true )).

fof(t22_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v13_lattices(A)
       => ! [B] :
            ( m1_filter_0(B,A)
           => ~ ( B != u1_struct_0(A)
                & ! [C] :
                    ( m1_filter_0(C,A)
                   => ~ ( r1_tarski(B,C)
                        & v1_filter_0(C,A) ) ) ) ) ) ) )).

fof(t23_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ ( ~ ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => k4_lattices(A,B,C) = B )
              & k2_filter_0(A,B) = u1_struct_0(A) ) ) ) )).

fof(t24_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v13_lattices(A)
              & l3_lattices(A)
              & B != k5_lattices(A)
              & ! [C] :
                  ( m1_filter_0(C,A)
                 => ~ ( r2_hidden(B,C)
                      & v1_filter_0(C,A) ) ) ) ) ) )).

fof(d5_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_filter_0(C,A)
             => ( C = k3_filter_0(A,B)
              <=> ( r1_tarski(B,C)
                  & ! [D] :
                      ( m1_filter_0(D,A)
                     => ( r1_tarski(B,D)
                       => r1_tarski(C,D) ) ) ) ) ) ) ) )).

fof(t25_filter_0,axiom,(
    $true )).

fof(t26_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => k3_filter_0(A,B) = B ) ) )).

fof(t27_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r1_tarski(B,C)
               => r1_tarski(k3_filter_0(A,B),k3_filter_0(A,C)) ) ) ) ) )).

fof(t28_filter_0,axiom,(
    $true )).

fof(t29_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r2_hidden(B,C)
               => r1_tarski(k2_filter_0(A,B),k3_filter_0(A,C)) ) ) ) ) )).

fof(t30_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( C = k6_domain_1(u1_struct_0(A),B)
               => k3_filter_0(A,C) = k2_filter_0(A,B) ) ) ) ) )).

fof(t31_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v13_lattices(A)
              & l3_lattices(A)
              & r2_hidden(k5_lattices(A),B) )
           => ( k3_filter_0(A,B) = k1_filter_0(A)
              & k3_filter_0(A,B) = u1_struct_0(A) ) ) ) ) )).

fof(t32_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v13_lattices(A)
              & l3_lattices(A)
              & r2_hidden(k5_lattices(A),B) )
           => ( B = k1_filter_0(A)
              & B = u1_struct_0(A) ) ) ) ) )).

fof(d6_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( v2_filter_0(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k3_lattices(A,C,D),B)
                    <=> ( r2_hidden(C,B)
                        | r2_hidden(D,B) ) ) ) ) ) ) ) )).

fof(t33_filter_0,axiom,(
    $true )).

fof(t34_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A)
          & l3_lattices(A) )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r3_lattices(A,k4_lattices(A,B,k3_lattices(A,k7_lattices(A,B),C)),C)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r3_lattices(A,k4_lattices(A,B,D),C)
                       => r3_lattices(A,D,k3_lattices(A,k7_lattices(A,B),C)) ) ) ) ) ) ) ) )).

fof(d7_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v3_filter_0(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r1_lattices(A,k2_lattices(A,B,D),C)
                    & ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r1_lattices(A,k2_lattices(A,B,E),C)
                         => r1_lattices(A,E,D) ) ) ) ) ) ) ) )).

fof(d8_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( ~ v3_struct_0(A)
                  & v10_lattices(A)
                  & v3_filter_0(A)
                  & l3_lattices(A) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( D = k4_filter_0(A,B,C)
                    <=> ( r3_lattices(A,k4_lattices(A,B,D),C)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( r3_lattices(A,k4_lattices(A,B,E),C)
                             => r3_lattices(A,E,D) ) ) ) ) ) ) ) ) ) )).

fof(t35_filter_0,axiom,(
    $true )).

fof(t36_filter_0,axiom,(
    $true )).

fof(t37_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => v14_lattices(A) ) )).

fof(t38_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_filter_0(A,B,B) = k6_lattices(A) ) ) )).

fof(t39_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => v11_lattices(A) ) )).

fof(t40_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => v3_filter_0(A) ) )).

fof(t41_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_filter_0(D,A)
                 => ( ( r2_hidden(B,D)
                      & r2_hidden(k4_filter_0(A,B,C),D) )
                   => r2_hidden(C,D) ) ) ) ) ) )).

fof(t42_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_filter_0(D,A)
                 => ( r2_hidden(B,D)
                   => r2_hidden(k4_filter_0(A,C,B),D) ) ) ) ) ) )).

fof(t43_filter_0,axiom,(
    $true )).

fof(t44_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
                     => ( ( r2_hidden(B,D)
                          & r2_hidden(C,E) )
                       => ( r2_hidden(k4_lattices(A,B,C),k5_filter_0(A,D,E))
                          & r2_hidden(k4_lattices(A,C,B),k5_filter_0(A,D,E)) ) ) ) ) ) ) ) )).

fof(t45_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B,C] :
          ( ( ~ v1_xboole_0(C)
            & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [D] :
              ( ( ~ v1_xboole_0(D)
                & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
             => ~ ( r2_hidden(B,k5_filter_0(A,C,D))
                  & ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ~ ( B = k4_lattices(A,E,F)
                              & r2_hidden(E,C)
                              & r2_hidden(F,D) ) ) ) ) ) ) ) )).

fof(t46_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k5_filter_0(A,B,C) = k5_filter_0(A,C,B) ) ) ) )).

fof(t47_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),k3_filter_0(A,B),C))
                & k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,k3_filter_0(A,C))) ) ) ) ) )).

fof(t49_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( m1_filter_0(C,A)
             => ( r1_tarski(B,k5_filter_0(A,B,C))
                & r1_tarski(C,k5_filter_0(A,B,C)) ) ) ) ) )).

fof(t50_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( m1_filter_0(C,A)
             => k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k3_filter_0(A,k5_filter_0(A,B,C)) ) ) ) )).

fof(t51_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( m1_filter_0(C,A)
             => k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k6_filter_0(A,B,C) ) ) ) )).

fof(t52_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( m1_filter_0(C,A)
             => k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k7_filter_0(A,B,C) ) ) ) )).

fof(t53_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( r2_hidden(B,k3_filter_0(A,k4_subset_1(u1_struct_0(A),D,k6_domain_1(u1_struct_0(A),C))))
                   => r2_hidden(k4_filter_0(A,C,B),k3_filter_0(A,D)) ) ) ) ) ) )).

fof(t54_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_filter_0(E,A)
                     => ( ( r2_hidden(k4_filter_0(A,B,C),E)
                          & r2_hidden(k4_filter_0(A,C,D),E) )
                       => r2_hidden(k4_filter_0(A,B,D),E) ) ) ) ) ) ) )).

fof(t55_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_filter_0(A,B,C) = k3_lattices(A,k7_lattices(A,B),C) ) ) ) )).

fof(t56_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,B,C)
              <=> k4_lattices(A,B,k7_lattices(A,C)) = k5_lattices(A) ) ) ) ) )).

fof(t57_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( v1_filter_0(B,A)
          <=> ( B != u1_struct_0(A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( r2_hidden(C,B)
                    | r2_hidden(k7_lattices(A,C),B) ) ) ) ) ) ) )).

fof(t58_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ( B != k1_filter_0(A)
              & v2_filter_0(B,A) )
          <=> v1_filter_0(B,A) ) ) ) )).

fof(t59_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( v1_filter_0(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                <=> ~ r2_hidden(k7_lattices(A,C),B) ) ) ) ) ) )).

fof(t60_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != C
                  & ! [D] :
                      ( m1_filter_0(D,A)
                     => ~ ( v1_filter_0(D,A)
                          & ( ( r2_hidden(B,D)
                              & ~ r2_hidden(C,D) )
                            | ( ~ r2_hidden(B,D)
                              & r2_hidden(C,D) ) ) ) ) ) ) ) ) )).

fof(d10_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & l3_lattices(C) )
             => ( C = k8_filter_0(A,B)
              <=> ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(B,B),B)
                    & m2_relset_1(D,k2_zfmisc_1(B,B),B)
                    & ? [E] :
                        ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,B),B)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B)
                        & D = k1_realset1(u2_lattices(A),B)
                        & E = k1_realset1(u1_lattices(A),B)
                        & C = g3_lattices(B,D,E) ) ) ) ) ) ) )).

fof(t61_filter_0,axiom,(
    $true )).

fof(t62_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_lattices(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k8_filter_0(A,k1_filter_0(A)) = A ) )).

fof(t63_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( u1_struct_0(k8_filter_0(A,B)) = B
            & u2_lattices(k8_filter_0(A,B)) = k1_realset1(u2_lattices(A),B)
            & u1_lattices(k8_filter_0(A,B)) = k1_realset1(u1_lattices(A),B) ) ) ) )).

fof(t64_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_filter_0(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k8_filter_0(A,D)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k8_filter_0(A,D)))
                         => ( ( B = E
                              & C = F )
                           => ( k3_lattices(A,B,C) = k3_lattices(k8_filter_0(A,D),E,F)
                              & k4_lattices(A,B,C) = k4_lattices(k8_filter_0(A,D),E,F) ) ) ) ) ) ) ) ) )).

fof(t65_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_filter_0(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k8_filter_0(A,D)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k8_filter_0(A,D)))
                         => ( ( B = E
                              & C = F )
                           => ( r3_lattices(A,B,C)
                            <=> r3_lattices(k8_filter_0(A,D),E,F) ) ) ) ) ) ) ) ) )).

fof(t66_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( v14_lattices(A)
           => v14_lattices(k8_filter_0(A,B)) ) ) ) )).

fof(t67_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( v12_lattices(A)
           => v12_lattices(k8_filter_0(A,B)) ) ) ) )).

fof(t68_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( v11_lattices(A)
           => v11_lattices(k8_filter_0(A,B)) ) ) ) )).

fof(t69_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v3_filter_0(A)
              & l3_lattices(A) )
           => v3_filter_0(k8_filter_0(A,B)) ) ) ) )).

fof(t70_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v13_lattices(k8_filter_0(A,k2_filter_0(A,B))) ) ) )).

fof(t71_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_lattices(k8_filter_0(A,k2_filter_0(A,B))) = B ) ) )).

fof(t72_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v14_lattices(A)
           => k6_lattices(k8_filter_0(A,k2_filter_0(A,B))) = k6_lattices(A) ) ) ) )).

fof(t73_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v14_lattices(A)
              & l3_lattices(A) )
           => v15_lattices(k8_filter_0(A,k2_filter_0(A,B))) ) ) ) )).

fof(t74_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v15_lattices(A)
              & v16_lattices(A)
              & l3_lattices(A)
              & ~ v3_struct_0(A)
              & v10_lattices(A)
              & v12_lattices(A)
              & l3_lattices(A) )
           => ( ~ v3_struct_0(k8_filter_0(A,k2_filter_0(A,B)))
              & v10_lattices(k8_filter_0(A,k2_filter_0(A,B)))
              & v15_lattices(k8_filter_0(A,k2_filter_0(A,B)))
              & v16_lattices(k8_filter_0(A,k2_filter_0(A,B)))
              & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) ) ) ) ) )).

fof(t75_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v17_lattices(A)
              & l3_lattices(A) )
           => ( ~ v3_struct_0(k8_filter_0(A,k2_filter_0(A,B)))
              & v10_lattices(k8_filter_0(A,k2_filter_0(A,B)))
              & v17_lattices(k8_filter_0(A,k2_filter_0(A,B)))
              & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) ) ) ) ) )).

fof(d11_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_filter_0(A,B,C) = k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,C,B)) ) ) ) )).

fof(t76_filter_0,axiom,(
    $true )).

fof(t77_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_filter_0(A,B,C) = k9_filter_0(A,C,B) ) ) ) )).

fof(t78_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_filter_0(E,A)
                     => ( ( r2_hidden(k9_filter_0(A,B,C),E)
                          & r2_hidden(k9_filter_0(A,C,D),E) )
                       => r2_hidden(k9_filter_0(A,B,D),E) ) ) ) ) ) ) )).

fof(d12_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( v1_relat_1(C)
             => ( C = k10_filter_0(A,B)
              <=> ( r1_tarski(k3_relat_1(C),u1_struct_0(A))
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E),C)
                          <=> r2_hidden(k9_filter_0(A,D,E),B) ) ) ) ) ) ) ) ) )).

fof(t79_filter_0,axiom,(
    $true )).

fof(t80_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(t81_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v3_filter_0(A)
              & l3_lattices(A) )
           => r1_relat_2(k10_filter_0(A,B),u1_struct_0(A)) ) ) ) )).

fof(t82_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => r3_relat_2(k10_filter_0(A,B),u1_struct_0(A)) ) ) )).

fof(t83_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v3_filter_0(A)
              & l3_lattices(A) )
           => r8_relat_2(k10_filter_0(A,B),u1_struct_0(A)) ) ) ) )).

fof(t84_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v3_filter_0(A)
              & l3_lattices(A) )
           => ( v3_relat_2(k10_filter_0(A,B))
              & v8_relat_2(k10_filter_0(A,B))
              & v1_partfun1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A))
              & m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) )).

fof(t85_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v3_filter_0(A)
              & l3_lattices(A) )
           => k3_relat_1(k10_filter_0(A,B)) = u1_struct_0(A) ) ) ) )).

fof(d13_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_filter_0(A,B,C,D)
                  <=> r2_hidden(k9_filter_0(A,C,D),B) ) ) ) ) ) )).

fof(t86_filter_0,axiom,(
    $true )).

fof(t87_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_filter_0(D,A)
                 => ( r1_filter_0(A,D,B,C)
                  <=> r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k10_filter_0(A,D)) ) ) ) ) ) )).

fof(t88_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v3_filter_0(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_filter_0(E,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( r1_filter_0(C,E,D,D)
                            & r1_filter_0(A,B,F,F) ) ) ) ) ) ) ) )).

fof(t89_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_filter_0(D,A)
                 => ( r1_filter_0(A,D,B,C)
                   => r1_filter_0(A,D,C,B) ) ) ) ) ) )).

fof(t90_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v3_filter_0(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ! [G] :
                              ( m1_filter_0(G,C)
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(A))
                                         => ( ( ( r1_filter_0(C,G,D,E)
                                                & r1_filter_0(C,G,E,F) )
                                             => r1_filter_0(C,G,D,F) )
                                            & ( ( r1_filter_0(A,B,H,I)
                                                & r1_filter_0(A,B,I,J) )
                                             => r1_filter_0(A,B,H,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_m1_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(existence_m1_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ? [B] : m1_filter_0(B,A) ) )).

fof(dt_k1_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => m1_filter_0(k1_filter_0(A),A) ) )).

fof(dt_k2_filter_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_filter_0(k2_filter_0(A,B),A) ) )).

fof(dt_k3_filter_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_filter_0(k3_filter_0(A,B),A) ) )).

fof(dt_k4_filter_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_filter_0(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k5_filter_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k5_filter_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k6_filter_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A)
        & m1_filter_0(C,A) )
     => m1_filter_0(k6_filter_0(A,B,C),A) ) )).

fof(redefinition_k6_filter_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A)
        & m1_filter_0(C,A) )
     => k6_filter_0(A,B,C) = k5_filter_0(A,B,C) ) )).

fof(dt_k7_filter_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A)
        & m1_filter_0(C,A) )
     => m1_filter_0(k7_filter_0(A,B,C),A) ) )).

fof(redefinition_k7_filter_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A)
        & m1_filter_0(C,A) )
     => k7_filter_0(A,B,C) = k5_filter_0(A,B,C) ) )).

fof(dt_k8_filter_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A) )
     => ( ~ v3_struct_0(k8_filter_0(A,B))
        & v10_lattices(k8_filter_0(A,B))
        & l3_lattices(k8_filter_0(A,B)) ) ) )).

fof(dt_k9_filter_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k9_filter_0(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k10_filter_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A) )
     => v1_relat_1(k10_filter_0(A,B)) ) )).

fof(dt_k11_filter_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A)
        & m1_filter_0(B,A) )
     => ( v3_relat_2(k11_filter_0(A,B))
        & v8_relat_2(k11_filter_0(A,B))
        & v1_partfun1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(redefinition_k11_filter_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A)
        & m1_filter_0(B,A) )
     => k11_filter_0(A,B) = k10_filter_0(A,B) ) )).

fof(dt_k12_filter_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A) )
     => ( v3_relat_2(k12_filter_0(A,B))
        & v8_relat_2(k12_filter_0(A,B))
        & v1_partfun1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(redefinition_k12_filter_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A) )
     => k12_filter_0(A,B) = k10_filter_0(A,B) ) )).

fof(d3_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_filter_0(A,B) = a_2_0_filter_0(A,B) ) ) )).

fof(d9_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k5_filter_0(A,B,C) = a_3_0_filter_0(A,B,C) ) ) ) )).

fof(t48_filter_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( m1_filter_0(C,A)
             => k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = a_3_1_filter_0(A,B,C) ) ) ) )).

fof(fraenkel_a_2_0_filter_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_0_filter_0(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r3_lattices(B,C,D) ) ) ) )).

fof(fraenkel_a_3_0_filter_0,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & ~ v1_xboole_0(D)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_0_filter_0(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,u1_struct_0(B))
            & m1_subset_1(F,u1_struct_0(B))
            & A = k4_lattices(B,E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) )).

fof(fraenkel_a_3_1_filter_0,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B)
        & m1_filter_0(C,B)
        & m1_filter_0(D,B) )
     => ( r2_hidden(A,a_3_1_filter_0(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = E
            & ? [F] :
                ( m1_subset_1(F,u1_struct_0(B))
                & ? [G] :
                    ( m1_subset_1(G,u1_struct_0(B))
                    & r3_lattices(B,k4_lattices(B,F,G),E)
                    & r2_hidden(F,C)
                    & r2_hidden(G,D) ) ) ) ) ) )).
%------------------------------------------------------------------------------